Suppose is differentiable and invertible with and

MATHEMATICS · Subjective · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

Suppose ff is differentiable and invertible with f(2)=5f(2)=5 and f′(2)=−3f'(2)=-3. Let gg be differentiable with g′(2)=7g'(2)=7. Define k(x)=g(f−1(x))k(x)=g\bigl(f^{-1}(x)\bigr). Determine k′(5)k'(5).

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